Cut-off Frequency
The Pipe Acoustics interface assumes plane wave propagation. This means that it cannot model the propagation of the higher order modes that can propagate above their cut-off frequency
f
c
. In a rectangular pipe of cross section width
w
i
and height
h
i
the cut-off frequency is
In a pipe of circular cross section (with radius
a
) the cut-off frequency is
where
α
'
mn
is the n’th zero of the differential of the Bessel function
J
’
m
(
x
) or order m. The first few values are
α
'
01
= 0,
α
'
02
= 3.83,
α
'
11
= 1.84, and
α
'
21
= 3.05 (see
Ref. 1
and
Ref. 5
for further details).
